Subgroups — #21426372

Order 7552.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837804	C₂	1	1	yes	maximal, characteristic
2	#16837229	C₂	1	2	yes	maximal
3	#16837227	C₂	1	2	yes	maximal
4	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#499	C₂	1	1	yes	maximal, characteristic
6	#14273719	—	2	1	no	—
7	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
9	#14273661	C₂²	1	2	yes	—
10	#14273659	—	2	1	no	—
11	#125×C₅₉	—	2	1	no	—
12	#107×C₅₉	C₂²	1	2	yes	—
13	#106×C₅₉	—	2	1	no	—
14	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₅₉	—	2	2	no	—
18	C₄⋊C₄×C₅₉	—	4	2	no	—
19	C₄²×C₅₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₅₉	—	2	2	no	—
21	Dic₅₉⋊C₄	—	4	2	no	—
22	C₅₉⋊C₁₆	Q₈	1	2	yes	—
23	C₅₉⋊C₁₆	Q₈	1	2	yes	—
24	C₂×C₄×C₅₉	—	4	2	no	—
25	C₂×C₄×C₅₉	D₈	1	2	yes	—
26	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₅₉	—	4	2	no	—
28	C₈×C₅₉	Q₁₆	1	2	yes	—
29	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
32	C₄×C₅₉	—	2	2	no	—
33	C₄×C₅₉	—	8	2	no	—
34	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
35	C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₅₉	—	8	2	no	—
37	#2253	—	59	1	no	maximal, Sylow
38	C₂×C₅₉	#500	1	1	yes	characteristic
39	C₂×C₅₉	#508	1	2	yes	—
40	#499	—	59	1	no	—
41	#499	D₅₉	1	1	yes	characteristic
42	#367	—	59	2	no	—
43	#366	—	59	2	no	—
44	C₄×C₁₆	—	59	1	no	—
45	C₅₉	#2253	1	1	yes	characteristic, complemented, Sylow
46	#125	—	2	1	no	—
47	#125	—	118	1	no	—
48	C₂×C₁₆	—	59	1	no	—
49	C₂×C₁₆	—	59	1	no	—
50	#107	—	59	2	no	—
51	#107	C₂×D₅₉	1	2	yes	—
52	#106	—	2	1	no	—
53	#106	—	118	1	no	—
54	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
55	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	118	2	no	—
60	C₄⋊C₄	—	236	2	no	—
61	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
62	C₁₆	—	59	2	no	—
63	C₁₆	—	59	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	236	2	no	—
66	C₂×C₄	#11745669	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
68	C₈	#11745672	1	2	yes	—
69	C₈	Q₈×D₅₉	1	1	yes	characteristic
70	C₈	Q₈×D₅₉	1	1	yes	characteristic
71	C₂²	C₂×#11745669	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	472	2	no	—
75	C₄	#14273725	1	1	yes	characteristic
76	C₄	C₂×#11745672	1	1	yes	characteristic
77	C₂	#16837805	1	1	yes	characteristic
78	C₂	#16837832	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#499	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#499	D₅₉
hypocenter	C₅₉	#2253
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
45. C₅₉	#2253	semidirect